I've been seeing her mom for a while now, and we spend a fair bit of time at each other's places. My spare room is now pretty much my girlfriend's daughter's second bedroom.

The problem it my girlfriends daughter is really clingy and I would even say flirty towards me. At first I thought she just wanted attention or something, but it's clearly been moving more into the flirty territory as time has gone on.

She tries to hug me and a few times has even asked to sit in my lap. I've not let her sit in my lap of course, and I only ever hug her hello and goodbye, but I'm thinking I should probably stop that as well.

I told my girlfriend I was more than a little concerned but she said it's just a crush and that it's pretty normal. It doesn't feel normal to me. But there again I don't have any kids myself and as an only child I haven't really had anything to do with kids until I met my girlfriend.

Is my girlfriend right? Is it just a harmless crush?

What you describe sounds pretty normal to me.

A daughter often emulates her mother . So she may be showing the affection she sees her mother show.

She may also be seeking to fill the void left when the parents split if he was part of their lives as she was growing up.

Another possibility,
She may also just honestly like you.

I think your girl is correct in the "Harmless Crush" conclusion.

I also think it wise to check if in doubt in any similar situation. We will be here for any future matters arising like dealing with teenage girls, you may encounter.